Question: A brass measuring is correct at 15 degree Celsius, the volume obtained when the length of an object measured with the rule at 35 degree Celsius appears to be 841.4cm. what's the true length of the object?
To solve this problem, we need to use the coefficient of thermal expansion of brass which is 0.000019. This means that for every 1 degree Celsius increase in temperature, the length of the brass measuring rule will increase by 0.000019 times its original length.
Let's assume that the true length of the object is x.
At 15 degree Celsius, the brass measuring rule is correct which means that the length of the object measured with the rule is also x.
At 35 degree Celsius, the length of the brass measuring rule would have increased by (35-15) x 0.000019 x length of the brass measuring rule at 15 degree Celsius.
So, the new length of the brass measuring rule at 35 degree Celsius would be:
Length of brass measuring rule at 15 degree Celsius + (35-15) x 0.000019 x Length of the brass measuring rule at 15 degree Celsius
= Length of brass measuring rule at 15 degree Celsius + (20 x 0.000019 x Length of the brass measuring rule at 15 degree Celsius)
= Length of brass measuring rule at 15 degree Celsius + 0.00038 x Length of the brass measuring rule at 15 degree Celsius
= 1.00038 x Length of the brass measuring rule at 15 degree Celsius
Now, we know that the volume obtained when the length of an object measured with the rule at 35 degree Celsius appears to be 841.4cm. This means that:
Length of the object measured at 35 degree Celsius x Width of the object x Height of the object = 841.4
Since we are trying to find the true length of the object, we can assume that the width and height of the object are not affected by temperature.
So, we can write:
x x Width of the object x Height of the object = 841.4 / Length of the object measured at 35 degree Celsius
x x Width of the object x Height of the object = 841.4 / [(1.00038 x Length of the brass measuring rule at 15 degree Celsius)]
x = (841.4 / [(1.00038 x Length of the brass measuring rule at 15 degree Celsius)]) / (Width of the object x Height of the object)
Substituting the value of Length of the brass measuring rule at 15 degree Celsius = 1 cm, we get:
x = (841.4 / 1.00038) / (Width of the object x Height of the object)
x = 841.166 / (Width of the object x Height of the object)
Therefore, the true length of the object is 841.166 divided by the product of the width and height of the object.